Q:Is there a way to make this not case-sensitive?A:No, your best option in that case would be to use a loop and check each inventory name individually as in the following example:

string InventoryName(string name, integer type)
{//finds an item in a case insensitive fashion of the given type and returns its true name.
integer a = llGetInventoryType(name);
if(!~a)//a == INVENTORY_NONE
{//it should be noted that INVENTORY_NONE == INVENTORY_ALL == -1; which is why '!~a' works.
string lc_name = llToLower(name);
a = llGetInventoryNumber(type);
while(a)
{//(a = ~-a) is equivalent to --a, but runs faster.
if(llToLower(name = llGetInventoryName(type, a = ~-a)) == lc_name)
{//we found a match ^_^
return name;
}
}
}
elseif((a == type) ^ (!~type))//return name, aslong as a == type or type == INVENTORY_ALL
{//we already know that a != INVENTORY_NONE, but just incase we use xor instead of or.
return name;
}
return "";//no match ~_~
}
integer InventoryExists(string name, integer type)
{//only included to show how this type of check could be done if the value of 'type' is not constant and could be INVENTORY_ALL.
return (llGetInventoryType(name) == type) ^ (!~type);
}//Since INVENTORY_ALL == INVENTORY_NONE, the extra part on the end is required to invert the result.